This paper considers the Strongly Asynchronous, Slotted, Discrete Memoryless, Massive Access Channel (SAS-DM-MAC) in which the number of users, the number of messages, and the asynchronous window length grow exponentially with the coding blocklength with their respective exponents. A joint probability of error is enforced, ensuring that all the users' identities and messages are correctly identified and decoded. Achievability bounds are derived for the case that different users have similar channels, the case that users' channels can be chosen from a set which has polynomially many elements in the blocklength, and the case with no restriction on the users' channels. A general converse bound on the capacity region and a converse bound on the maximum growth rate of the number of users are derived. It is shown that reliable transmission with an exponential number of users with an exponential asynchronous exponent with joint error probability is possible at strictly positive rates.
Keywords: asynchronous communication; massive access; multiple access channels.